Problem: Solve for $p$, $ -\dfrac{10}{3p - 9} = \dfrac{5p - 1}{2p - 6} + \dfrac{3}{p - 3} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3p - 9$ $2p - 6$ and $p - 3$ The common denominator is $6p - 18$ To get $6p - 18$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ -\dfrac{10}{3p - 9} \times \dfrac{2}{2} = -\dfrac{20}{6p - 18} $ To get $6p - 18$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ \dfrac{5p - 1}{2p - 6} \times \dfrac{3}{3} = \dfrac{15p - 3}{6p - 18} $ To get $6p - 18$ in the denominator of the third term, multiply it by $\frac{6}{6}$ $ \dfrac{3}{p - 3} \times \dfrac{6}{6} = \dfrac{18}{6p - 18} $ This give us: $ -\dfrac{20}{6p - 18} = \dfrac{15p - 3}{6p - 18} + \dfrac{18}{6p - 18} $ If we multiply both sides of the equation by $6p - 18$ , we get: $ -20 = 15p - 3 + 18$ $ -20 = 15p + 15$ $ -35 = 15p $ $ p = -\dfrac{7}{3}$